This question has TWO separate parts and your answer will be TWO SEPARATE graphs.

Part $1$: Sketch a graph of a function $f(x)$ with the following properties:

a critical point at $x=-3$ and $f^{\text{'}}(-3)$ is undefied

a critical point at $x=4$ and $f^{\text{'}}(4)=0.$

That is the end of part $1.$

Part $2-$ This is a graph completely separate from the previous part. Sketch a graph with the following properties:

$f^{\text{'}}(x)<0$ on $(-,-4)U(5,).$

$f^{\text{'}}(x)>0$ on $(-4,5)$

$f^{\text{'}\text{'}}(x)>0$ on $(-,1)$

$f^{\text{'}\text{'}}(x)<0$ on $(1,)$